Place the chicken thighs in the bottom of the slow cooker. Drizzle with olive oil and season with salt and pepper.
Add the minced garlic, lemon zest, lemon juice, and rosemary sprigs on top of the chicken.
Pour the chicken broth around the chicken pieces.
Cover and cook on low for 5 hours.
Add the sliced mushrooms and asparagus pieces to the slow cooker. Stir gently to combine with the cooking liquid.
Cover and cook on low for 1 more hour until the vegetables are tender and the chicken reaches an internal temperature of 165 degrees.
Remove the rosemary sprigs before serving.